For this purpose, we attempt to design new GNN pre-training tasks that are able to learn node- and graph-level graph semantics in one single pre-training task.
Our solution is based on neural graph matching [1]}, [2]}, [3]}, a neural approach to learning structural correspondence among graphs. We present an illustrative example of our idea in Figure REF .
At each time, a pair of two associated graphs (e.g., with the same labels or augmented graphs) are given, and we evaluate whether the two graphs have similar structural properties. As a major advantage, neural graph matching
naturally combines node-level correspondence (e.g., \(v_1\)  to \(v_2\) ) and graph-level properties (e.g., whether containing shared substructure)
when establishing their correspondence.
That is the major reason why we adopt it as the GNN pre-training task.
Another merit of this approach is that a graph will correspond to different representations when paired with different graphs. As shown in this example, we will derive different representations for graph \(A\)  when paired with graph \(A_1\)  or \(A_2\) , since neural graph matching will enforce one graph to refer to another graph's information when learning graph representations. Therefore, we call the learned representations adaptive graph representations.
As a comparison, existing graph-level pre-training tasks usually adopt static graph representations.
